OFFSET
1,2
COMMENTS
From Gus Wiseman, Jul 22 2019: (Start)
These are numbers whose positions of 1's in their reversed binary expansion form a strict knapsack partition (A275972). The initial terms together with their corresponding partitions are:
1: (1)
2: (2)
3: (2,1)
4: (3)
5: (3,1)
6: (3,2)
8: (4)
9: (4,1)
10: (4,2)
11: (4,2,1)
12: (4,3)
14: (4,3,2)
16: (5)
17: (5,1)
18: (5,2)
19: (5,2,1)
20: (5,3)
(End)
EXAMPLE
14=2+4+8 so Partition(14) = [2,3,4], whose sub-sums are 0,2,3,4,5,6,7 and 14.
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[100], UnsameQ@@Total/@Subsets[bpe[#]]&] (* Gus Wiseman, Jul 22 2019 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Marc LeBrun, Jan 19 2001
STATUS
approved